Question

there are 12 brown socks and 6 blue socks in a drawer. in the dark, jason pulls out a sock and puts it on his right foot. then he pulls out another sock and puts it on his left foot. what is the probability that jason has two blue socks on his feet? 5/54 5/51 1/3 2/17

Explanation:

Step1: Calculate the total number of socks

The total number of socks is \(12 + 6=18\) socks.

Step2: Calculate the probability of picking the first blue sock

The probability of picking a blue sock first is \(\frac{6}{18}=\frac{1}{3}\).

Step3: Calculate the probability of picking the second blue sock

After picking one blue sock, there are \(6 - 1 = 5\) blue socks left and \(18- 1=17\) socks left. So the probability of picking a blue sock second is \(\frac{5}{17}\).

Step4: Calculate the combined probability

Since these are two - step dependent events, we multiply the probabilities. The probability of picking two blue socks is \(\frac{6}{18}\times\frac{5}{17}=\frac{5}{51}\).

Answer:

\(\frac{5}{51}\) (corresponding to the second option)